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A mathematical model of plasma membrane electrophysiology and calcium dynamics in vascular endothelial cells.


A mathematical model of plasma membrane electrophysiology and calcium dynamics in vascular endothelial cells. Am J Physiol Cell Physiol 293: C277–C293, 2007. First published April 25, 2007; doi:10.1152 ajpcell.00542.2006. Vascular endothelial cells (ECs) modulate smooth muscle cell (SMC) contractility, assisting in vascular tone regulation. Cytosolic Ca2+ concentration ([Ca2+]i) and membrane potential (Vm) play important roles in this process by controlling EC-dependent vasoactive signals and intercellular communication. The present mathematical model integrates plasmalemma electrophysiology and Ca2+ dynamics to investigate EC responses to different stimuli and the controversial relationship between [Ca2+]i and Vm. The model contains descriptions for the intracellular balance of major ionic species and the release of Ca2+ from intracellular stores. It also expands previous formulations by including more detailed transmembrane current descriptions. The model reproduces Vm responses to volume-regulated anion channel (VRAC) blockers and extracellular K+ concentration ([K+]o) challenges, predicting 1) that Vm changes upon VRAC blockade are [K+]o dependent and 2) a biphasic response of Vm to increasing [K+]o. Simulations of agonist-induced Ca2+ mobilization replicate experiments under control and Vm hyperpolarization blockade conditions. They show that peak [Ca2+]i is governed by store Ca2+ release while Ca2+ influx (and consequently Vm) impacts more the resting and plateau [Ca2+]i. The Vm sensitivity of rest and plateau [Ca2+]i is dictated by a [Ca2+]i “buffering” system capable of masking the Vm-dependent transmembrane Ca2+ influx. The model predicts plasma membrane Ca2+-ATPase and Ca2+ permeability as main players in this process. The heterogeneous Vm impact on [Ca2+]i may elucidate conflicting reports on how Vm influences EC Ca2+. The present study forms the basis for the development of multicellular EC-SMC models that can assist in understanding vascular autoregulation in health and disease.

Silva HS, Kapela A, Tsoukias NM.
Dept. of Biomedical Engineering, Florida International University,
10555 W. Flagler St., TEC 2674, Miami, FL 33174, USA.


The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

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 Silva HS, Kapela A, Tsoukias NM: A mathematical model of plasma membrane electrophysiology
  and calcium dynamics in vascular endothelial cells. Am J Physiol Cell Physiol 293:C277-C293, 2007  

 Kapela A, Bezerianos A, Tsoukias NM.: A mathematical model of Ca2+ dynamics in rat mesenteric
 smooth muscle cell: agonist and NO stimulation, J Theor Biol 253:238-260, 2008

 Kapela A, Bezerianos A, Tsoukias NM: A mathematical model of vasoreactivity in rat mesenteric arterioles: 
 I. Myoendothelial communication, MICROCIRC 16:8,(694-U69), 2009 
Key terms
calcium dynamics
gap junctions
ion channels
membrane potential
vascular tone regulation
calcium influx pathway(s)
plasma membrane Ca2+-ATPase

Please cite in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.